## What is the 'Periodic Interest Rate'

The periodic interest rate is the interest rate charged on a loan or realized on an investment over a specific period of time. Typically, lenders quote interest rates on an annual basis, but in most cases, the interest compounds more frequently than annually. As a result, the periodic interest rate is the annual interest rate divided by the number of compounding periods.

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## BREAKING DOWN 'Periodic Interest Rate'

For example, the interest on a mortgage is compounded or applied on a monthly basis. If the annual interest rate on a mortgage is 8%, the periodic interest rate used to calculate the interest assessed in any single month is 0.08 / 12 = 0.0067 or 0.67%. This means that every month, the remaining principal balance of the mortgage loan has a 0.67% interest rate applied to it.

## The Effect of Compounding Periods on Periodic Interest Rates

The number of compounding periods directly affects the periodic interest rate of an investment or a loan. For example, if an investment has an effective annual return of 12%, and it compounds every month, its periodic interest rate is 1%. If it compounds daily, its periodic interest rate is 0.00033 or the equivalent of 0.03%.

## The Effect of Compounding Periods on Investments

The more frequently an investment compounds, the more quickly it grows. To illustrate, imagine two options are available on a \$1,000 investment. Under option one, the investor receives an 8% annual interest rate and the investment compounds monthly. Under option two, the investor receives a 8.125% interest rate, compounded annually. By the end of a 10-year period, the \$1,000 investment under option grows to \$2,219.64, but under option two, it grows to \$2,184.04. Although the interest rate is higher in option two, the more frequent compounding of option one yields a greater return. The greater number of compounding periods allows interest to be earned on interest a greater number of times.

## Effective Rate Versus Periodic Rate

When discussing loans or investments, the annual interest rate quoted is typically a nominal interest rate, and the effective interest rate is the actual interest rate after the effects of compounding have been taken into account. To calculate a loan's effective annual interest rate, you need to know its nominal rate and the number of compounding periods. First, divide the nominal rate by the number of compounding periods. The result is the periodic rate. Add this number to 1 and take the sum by the power of the number of compounding interest rates. Subtract 1 from the product to get the effective interest rate.

For example, if a mortgage that compounds monthly has a nominal annual interest rate of 6%, its periodic rate is 0.5%. When you convert the percentage to a decimal and add 1, the sum is 1.005. This number to the 12th power is 1.0617. When you subtract 1 from this number, the difference is 0.0617 or 6.17%. The effective rate is slightly higher than the nominal rate.

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